Abstract

This paper presents a new complete orthonormal system of functions
defined on the interval [0,1] and whose supports shrink to nothing. This
system related to the construction of the Cantor ternary set. We defined the
canonical map ξ and proved the equivalence between this system and the Walsh
system. The generalized Cantor set with any dissection ratio is established
and the constructed system is defined in the general case.

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